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Chapter 5. FluidizationChapter 5. Fluidization 5.1 Fundamental * Δp vs. U Figure 5.1 Minimum...
Transcript of Chapter 5. FluidizationChapter 5. Fluidization 5.1 Fundamental * Δp vs. U Figure 5.1 Minimum...
Chapter 5. Fluidization
5.1 Fundamental
* Δ p vs. U Figure 5.1
Minimum (incipient) fluidization, U mf
From force balance
Net downward force
Δp= ( 1- ε )( ρ p- ρ g )H (1)
Net upward force
ΔpH
= 150( 1- ε ) 2
ε 3
μU
x 2sv
+ 1.751- ε
ε 3
ρgU
2
x sv (2)
Equating (1) and (2) at U=U mf
Ar=150( 1- ε )ε 3 Re mf+1.75
1ε 3 Re
2mf
where Ar≡ρgx
3sv (ρ p- ρ f)g
μ 2, Archimedes number
Re mf=ρfU mfx svμ
ε= 0.4, usually
More practically,
Wen and Yu(1966) for x sv > 1 0 0 μm
Ar= 1056Remf+159Re 2mf
Baeyens and Geldart(1974) for x < 1 0 0 μ m
U mf=( ρ p- ρ f)
0.934g 0.934x 1.8
1110μ 0.87ρ 0.066f
5.2 Relevant Powder and Particle Properties
- Absolute density: materials property
- Particle density: Figure 5.2
- Bed density
* Sieve diameter, x p , x v= 1.13x p
mean x p=1
∑m i/x i
5.3 Bubbling and Non-Bubbling Fluidization
Types of Fluidization
Various types of fluidized beds
- Bubbling fluidized bed : Figure 5.3 for Group B particles
- Liquid fluidization: Figure 5.4
5.4 Classification of Powders
Geldart(1974) Figure 5.6
Table 5.1
Group A : Nonbubbling for U m f < U < U m b
where
U mb= 2.07 exp (0.716F ) [xρ 0.06
g
μ 0.347 ] where F : fraction of powder less than 45 μm
Bubbling for U > U m b
Maximum bubble size
d Bv, max =2g
(U T2.7 )2
Group B : Bubbling for U > U m f
No maximum in bubble size
Slugging ( d B≥13D) - Figure 5.8 (right)
Tagi and Muchi (1952)
In order to avoid slug formation
(H m f
D )≤ 1.9
( ρ p x p )0.3
Slug forms when (H m f
D ) > 1 . 9
( ρ p x p )0 . 3
and
U > U mf+0.16(1.3 4D 0.175-H mf)2+ 0.07( gD ) 1/2
Group D : Spoutable
Group C : Subject to channeling in large diameter-bed
5.5 Expansion of a Fluidized Bed
(1) Nonbubbling Fluidized Bed
Upward superficial fluid velocity(or volumetric flux)
U= U Tε2f(ε) =U T
ε n
For Re p≤0.3, n= 4.65
For Re p≥500, n= 2.4
Assuming conservation of bed mass, M B
M B= (1- ε )ρ pAH
∴ ( 1- ε 1 )ρ pAH 1 = ( 1- ε 2 )ρ pAH 2
∴H 2
H 1=
1- ε 1
1- ε 2
Worked Example 5.1
(2) Bubbling Fluidized Bed
The bed is assumed to consist of two phases:
- Dense (particulate, emulsion) phase : a state of minimum
fluidization
- Lean (bubble) phase : flow of gas in excess of minimum
fluidization as bubbles
Gas flow as bubbles= Q-Qmf= (U-Umf )A
Gas flow in the emulsion phase=Qmf=UmfA
εB=
H-HmfH
=QBAU B
=U-UmfU B
* Mean bed voidage, 1- ε= ( 1- ε B )( 1- ε mf)
* Bubble Size and Rise Velocity
U B= Φ B (gd Bv )1/2
where ΦB= function of D
For group B
d Bv=0.54
g 0.2 (U-U mf )0.4(L+4N - 1/2 ) 0.8
where N : the number of holes/m2
L : distance above the distributor
5.6 Entrainment
- Carryover, elutriation
Zone above fluidized bed (Freeboard) - Figure 5.11
- Splash zone
- Transport disengagement zone
Transport disengagement height,
TDH from Figure 5.12 or
TDH= 4.47d 0.5Bvs
- Dilute-phase transport zone
Worked Example 5.1
Instantaneous entrainment rate of size x i
R i=-ddt
(MBmBi)=K*ihAm Bi
where M B: total mass of solids in the bed
A: area of bed surface
m Bi: fraction of bed mass with size x i at time t
K *ih: elutriation constant
Total rate of entrainment
R T=-ddt
[∑(MBm Bi)]=∑K*ihAm Bi
K*i∞: K *
ih above TDH - (5.45) and (5.46)
Worked Example 5.2
5.7 Heat transfer in Fluidized Bed
Heat transfer between particles and gas
Nu= 0.03Re 1.3p ( Re p≺50)
where Nu=h gpx
k g
L 0.5 : L for
T g-T sT g0-T s
=0.5
Very short(0.95mm~5mm)
Heat transfer between surface and bed
h = h p c + h g c + h r
particle gas radiation convection convection
Figure 5.14: h pc is controlled by k g
Figure 5.15: maximum occurs by blanket of bubbles
When U > ( 2 ∼ 3 )×U m f
For group B powders
h max = 35.8k 0.6gρ 0.2p
x0.36
, W/m2K
For group A powders
Nu max = 0.157Ar 0.475
5.8 Applications of Fluidized Beds
Advantages
- Liquid-like behavior, easy to control and automate
- Rapid mixing, uniform temperature and concentration
- Resists rapid temperature changes, hence responds slowly to
changes in operating conditions and avoids temperature runaway
with exothermic reactions
- Circulate solids between fluidized beds for heat exchange
- Applicable for large or small scale operations
- Heat and mass transfer rates are high, requiring smaller
surfaces
Disadvantages
- Bubbling beds are difficult to predict and are less efficient
- Rapid mixing of solids causes nonuniform residence times for
continuous flow reactors
- Particle comminution(breakup) is common
- Pipe and vessel walls erode to collisions by particles
(1) Physical Processes
Drying / Mixing / Granulation / Coating / Heat exchanger/
Adsorption(Desorption)
Figure 5.17
(2) Chemical Processes
Table 5.2
Figure 5.18 Fluidized catalytic cracker
5.9 A Simple Model for the Bubbling Fluidized Bed
Reactor
Figure 5.19
Orcutt et al(1962)
Form the overall mass balance on the reactant + shell mass balance
1-C HC 0
= (1- βe - χ)-
( 1- βe - χ ) 2
kH mf( 1- ε p )
U+ (1- β e - χ)
C BH= C P+ (C 0-C P) exp [- χ ]
C P=C 0[U-(U-U mf )e
- χ]
kH mf(1- ε P )+ [U (U-U mf)e- χ]
CH=UmfC P+(U-Umf)CBH
U
where C 0 : concentration of reactant at distributor
C H : concentration of reactant leaving the reactor(H)
C B : concentration of the reactant in the bubble phase
C P : concentration of the reactant in the particulate phase
β=U-UmfU
and χ=K cH
U B
where K c: mass transfer coefficient of the reactant from particulate
phase
Figure 5.20
Worked Example 5.3